Leading corrections to the compton profiles beyond the impulse approximation: second-order correction

Second-order corrections to the impulse-approximation Compton profiles of some inert atomic species (He, Ne, Ar, and Kr) are obtained by applying the theory due to Gasser, Tavard and others to a density functional model, as demonstrated recently for the first-order effect by Pathak, Kshirsagar, Hoffmeyer and Thakkar. The cumulative (first plus second) correction, for moderate momentum transfers (to the electron in the Compton process) is seen to bring out an appreciable structural change when augmented to the zeroth-order impulse profile. It is observed that the sign of the peak second-order correction is correlated to the orbital angular momentum and magnetic quantum numbers, whereby an empirical rule analogous to that of the behavior of the first-order correction is discovered.